(Bug #1)
- In the tree navigator right-click on table "test1" and select "Edit" from popup menu - "Edit table" window appears.
- Click on "Indexes" (in the tree in left panel)
- Next click on "DDL" (or something else) in the tree in left panel - error message appears "Index TEST1_PK_I is defined identically to constraint TEST1_PK"
What is wrong? Of course index TEST1 PK I is defined identically to constraint TEST1_PK, but it is not an error.

(Bug #2)
- In the tree navigator right-click on table "test1" and select "Edit" from popup menu - "Edit table" window appears.
- In left panel in tree select "Columns" (it is selected by default)
- Add comment to column "ID" - for example "Test comment"
- In left panel in tree select "DDL" - now I see two times the same SQL command as follows:

If you click on the Help button in the Table editor, under Indexes pane you will see the following caveat:

(Note, however, that this display does not include any indexes related to primary key and unique key constraints.)

Creating both an index and primary key constraint on the same column with different names seems to lead to the conditions you mention. If you create just the primary key constraint, or rename the index to match the primary key constraint, no index will appear in the editor per the help caveat noted above.

+"If you create just the primary key constraint, or rename the index to match the primary key constraint, no index will appear in the editor per the help caveat noted above."+

It is some kind of solution - but for newly created tables only. And it means that I must obey naming rules which SQL Developer ("Edit table" wizard) likes...

But what about hundreds of tables that exists already with different index name and PK constraint name? Renaming PK indexes in all of them sounds not good.
But without doing this they will be not editable in "Edit table" (as soon as I click on "Indexes" page)